Tense is the time in which your story takes place. And no, you in the back about to raise your hand, I don't mean 1899. Tense is the difference between reading something that takes place right now and something that happened awhile ago.

Present tense — Just like it sounds, it's something that happens as you speak. I'm writing this in the present tense. (Technically, I'm writing this in the present tense, with a bizarre mix of first- and second-person narration...) Indicators that you're in the present tense are verbs that are immediate—we run instead of ran, or even we are running. An example:

"You was out late," Racetrack notes, as we walk towards the bathroom to shave and get cleaned up a bit.
Blink smirks that adorable obnoxious smirk of his, the one that gets him in trouble, and Jack jumps up behind him. "What was her name, huh?" he demands. "You meet another blond?"
"Redhead," he says. "Redhead, green eyes, freckles... Gorgeous, Jacky, I mean it. Like Medda, if Medda was sixteen an' innocent."
"Bet she ain't innocent no more," Race says, and he and Blink play fight a bit. We stop in front of the mirror and lather up, then begin to shave with razors so used they barely make a difference.

You get the idea. Present tense gives things a more immediate feeling. It can be harder to write for a lot of people, so use it carefully.

Past Tense — Again, just what it sounds like. A story in the past tense is already finished, and being narrated after the fact. Similarly, indicators are verbs that are finished; we ran instead of run, I thought instead of think, etc.

Blink glanced up and shrugged. That was his usual answer; he'd say he didn't want to talk, or he'd shrug, and a minute later he'd start talking anyway. Mush slid down the back wall of the lodging house to sit next to his friend, and glanced around. He wondered for a moment how many conversations they'd had back here. It was more private in this side alley than out in the square in front of the lodging house, and usually also more private than in the house itself.

In the story, the events have already happened. Blink and Mush had this talk awhile ago, they aren't having it right now.

Generally, stories are told in the past tense. It's easier to read and easier to write, but that doesn't mean it's always the best. Furthermore, you can do first-person stories in the past tense or third-person stories in the present, though I don't have examples of them. I've found that present tense flows much better in the first-person, but that's personal preference.

Writing well means finding your own voice. Experiment, trying writing the same scene in a number of different ways. Figure out which one fits the story best and gives it the feeling you want it to have.

However, if you're unsure, stick with a third-person past tense story. It's about the easiest to do well.